Spectral Analysis 2 – The Fourier Transform in Modern Communications☆

This chapter helps the reader to understand the difference between periodic and nonperiodic signals and to become familiar with the Fourier transform. It explains how to apply the Fourier transform to the spectral analysis of nonperiodic signals. The chapter examines the main Fourier transform pairs and the main properties of the Fourier transform. It provides study examples of applications of the Fourier transform to the spectral analysis of various nonperiodic signals and systems. The chapter also discusses four types of signals – continuous periodic, continuous nonperiodic, discrete periodic, and discrete nonperiodic. It also discusses four types of the Fourier tools: continuous‐time Fourier series, continuous‐time Fourier transform, discrete Fourier transform (DFT), and discrete‐time Fourier transform. The chapter also why only DFT can be employed for digital signal processing and how DFT can be applied for the spectral analysis of both discrete periodic and discrete nonperiodic signals.